Exactly, the idea is that Elijah would return since he never died(chariot of fire). People thought John the Baptist was Elijah, but again, this is description not prescription.
I seem to recall a passage going something like this:
There is but one life (death?) for man,
and after this, The Judgement.
Don’t know the chapter or verse, but it seems to definitely refute reincarnation.
Which leads me to question how Christ is supposed to return.